(Q9)Find the roots of the following quadratic equations, if they exist.

(i)x2 + 4x + 5 = 0 (ii)2x2 -2√2x + 1 = 0

(i) x2 + 4x + 5 = 0. Here, a = 1, b = 4, c = 5. So, b2-4ac= - = -< 0

Since the square of a real number cannot be negative, therefore √(b2-4ac) will not have any real value.

So, there are no real roots for the given question.

(ii) 2x2 -2√x + 1 = -0 Here, a = 2, b = -2√2, c = 1

So, b2-4ac=-8=

Therefore, x =
2√2 ±√
4
 =
√2
2
± i.e x=
1
√
So,the roots are
1
√
 ,
1
√
 .